频率域弹性波方程全波形地震成像快速算法研究

Using elastic wave equation to carry out the full waveform inversion is of important scientific research value and arises in various application areas, which should be the development trend of the future full waveform inversion research in seismic exploration. However, the huge computation and multiple local minima of the elastic wave full waveform inversion limit its wide application in the field of seismic exploration. Hence, it is completely necessary to comprehensively carry out the fast algorithms for the elastic wave full waveform inversion. In this project, we mainly consider the efficient forward and inversion algorithms based on elastic wave equation, including: 1) Based on the technique of the hierarchically semi-separable matrix, we develop an efficient and scalable forward modeling algorithm; 2) Based on the Helmholtz wavefield decomposition principle, the approximate global optimization algorithm will be studied deeply to provide a good initial model for the full waveform inversion methods in frequency domain, solving the challenge of multiple local minima; 3) We also conduct the research of extended finite-difference contrast source inversion method in elastic medium to provide the high resolution reconstructions for the inverted parameters. Numerical results are illustrated to verify the validity of this inversion method. The project aims to make a great progress in the investigations of the fast forward modeling algorithm, the parallel computing, initial model building, and the inversion algorithm.

利用弹性波方程进行全波形反演，具有重要的科研价值和广泛的实际应用背景，是未来全波形反演地震勘探技术发展的必然趋势。然而，其巨大的计算量和多局部极值，阻碍了其在实际地震勘探领域的广泛应用。因此对弹性波全波形反演算法进行深入研究是完全有必要的。本项目以弹性波方程为理论模型，开展快速高效的弹性波全波形正反演算法研究，研究内容主要包括：1）基于分层半可分矩阵低秩分解技术，构造可扩展性好且快速高效的正演算法；2）基于Helmholtz波场分解理论，深入研究近似全局优化算法，为频率域全波形反演提供良好的初始模型，解决多局部极值难题；3）开展弹性波扩展有限差分对比源反演算法研究，实现重构参数的精细化快速反演，并通过数值模拟结果来验证方法的有效性。项目预期拟在快速正演模拟与并行计算、初始模型构建以及反演算法等方面取得较大的进展。

利用波动方程相关理论和地表接收的地震数据定量重构地层结构，以实现对复杂地质构造的高精细全波形反演具有重要的理论和实际意义。然而，全波形反演的大规模计算和多局部极值，阻碍了其在实际地震勘探领域的广泛应用。针对全波形反演的大规模计算和多局部极值问题，本项目开展了全波形正反演快速算法研究，以降低计算量、提高计算效率和重构精度。..针对正演大规模计算问题，本项目基于分层半可分矩阵低秩分解理论，给出了快速高效的正演方法，并进行数值实验验证了方法的有效性和高效性。针对多局部极值问题，提出了基于目标函数Hessian信息的信赖域和线搜索截断Newton反演方法，提出了基于深度神经网络重参数化的正则化反演方法，实现了目标地质构造体的快速高精细反演。数值实验表明，本项目提出的反演方法能有效求解复杂构造（高速度比和多散射波场问题）的全波形反演问题。此外，本项目提出的正反演理论和方法具有一般性和普适性，该理论和方法可以用于医学领域的超声成像问题。